vector analysis integrals

question.

if F(x,y) = f(x,y)i + g(x,y)j

f and g are continuous on an open connected region D.

a) what can you say about the work integrals of F along paths in D if

F = del(phi ), for some function phi(x,y)?

b) what can you say about F and work integral of F along paths in D if fsuby=gsubx throughout D?

What assumptions must be made about D?

C) given F(x,y) = (e^y +ye^x )i +(xe^y +e^x) j.

Compute the integral of C F dot dr if C is the path from (0,0) to (1,0) that follows the spiral r = theta /4pi.

Thank you!